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  • Letter
  • Open Access

Microscopic origin of temperature-dependent magnetism in spin-orbit-coupled transition metal compounds

Ying Li1,*, Ram Seshadri2, Stephen D. Wilson2, Anthony K. Cheetham3,4, and Roser Valentí5,†

  • *Contact author: yingli1227@xjtu.edu.cn
  • †Contact author: valenti@itp.uni-frankfurt.de
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Phys. Rev. Research 7, L012083 – Published 28 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012083

Abstract

A few 4d and 5d transition metal compounds with various electron fillings were recently found to exhibit magnetic susceptibilities χ and magnetic moments that deviate from the well-established Kotani model. This model has been considered for decades to be the canonical expression for descriing the temperature dependence of magnetism in systems with nonnegligible spin-orbit coupling effects. In this paper, we uncover the origin of such discrepancies and determine the applicability and limitations of the Kotani model by calculating the temperature dependence of the magnetic moments of a series of 4d (Ru-based) and 5d (W-based) systems at different electron fillings. For this purpose, we perform exact diagonalization of ab initio-derived relativistic multiorbital Hubbard models on finite clusters and compute their magnetic susceptibilities. Comparison with experimentally measured magnetic properties indicates that contributions such as a temperature-independent χ0 background, crystal field effects, Coulomb and Hund's couplings, and intersite interactions—not included in the Kotani model—are especially crucial for correctly describing the temperature dependence of χ and magnetic moments at various electron fillings in these systems. Based on our results, we propose a generalized approach beyond the Kotani model to accurately describe their magnetism.

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Phys. Rev. Research 7, L012083– Published 28 March, 2025
  • Received 3 April 2024
  • Accepted 26 February 2025
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